Question:
Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is
Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is
Updated On: Sep 30, 2024
- 2 : 5
- 4 : 9
- 3 : 8
- 1 : 3
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct answer is (D):
Let the area of ABCD be 100. Side of ABCD = 10 Area of EFGH is 62.5 => Side of EFGH = √62.5
Triangles AEH, BFE, CGF and DHG are congruent by ASA.
Let AE = BF = CG = DH = x; EB = FC = DG = AH = 10 -xx
AE2+ AH2 = EH2
x2+(10-x)2=(√62.5)2
Solving, x = 2.5 or 7.5
Since it’s given that CG is longer than EB, CG = 7.5 and EB = 2.5.
Therefore, EB : CG = 1 : 3
Was this answer helpful?
0
0
Top Questions on Geometry
- The equation of chord AB of ellipse \(2x^2 + y^2 = 1\) is \(x - y + 1 = 0\). If O is the origin, then \(\angle AOB =\)
In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?
- Let the sum of the focal distances of the point $ P(4, 3) $ on the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be $ 8\sqrt{\frac{5}{3}} $. If for $ H $, the length of the latus rectum is $ \ell $ and the product of the focal distances of the point $ P $ is $ m $, then $ 9\ell^2 + 6m $ is equal to:
- Let for two distinct values of $ p $, the lines $ y = x + p $ touch the ellipse $ E: \frac{x^2}{4} + \frac{y^2}{9} = 1 $ at the points $ A $ and $ B $. Let the line $ y = x $ intersect $ E $ at the points $ C $ and $ D $. Then the area of the quadrilateral $ ABCD $ is equal to:
The center of a circle $ C $ is at the center of the ellipse $ E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $, where $ a>b $. Let $ C $ pass through the foci $ F_1 $ and $ F_2 $ of $ E $ such that the circle $ C $ and the ellipse $ E $ intersect at four points. Let $ P $ be one of these four points. If the area of the triangle $ PF_1F_2 $ is 30 and the length of the major axis of $ E $ is 17, then the distance between the foci of $ E $ is:
View More Questions
Questions Asked in CAT exam
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Understanding central Asia’s role helps developments make more sense not only across Asia but in Europe, the Americas and Africa.
Paragraph: The nations of the Silk Roads are sometimes called ‘developing countries’, but they are actually some of the world’s most highly developed countries, the very crossroads of civilization, in advanced states of disrepair. ___(1)___. These countries lie at the centre of global affairs: they have since the beginning of history. Running across the spine of Asia, they form a web of connections fanning out in every direction, routes along which pilgrims and warriors, nomads and merchants have travelled, goods and produce have been bought and sold, and ideas exchanged, adapted and refined. ___(2)___ .They have carried not only prosperity, but also death and violence, disease and disaster. ___(3)___. The Silk Roads are the world’s central nervous system, connecting otherwise far-flung peoples and places…. ___(4)___. It allows us to see patterns and links, causes and effects that remain invisible if one looks only at Europe, or North America.- CAT - 2024
- Para Completion
- Let $x$, $y$, and $z$ be real numbers satisfying
\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?- CAT - 2024
- Algebra
- The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Certain codes may, of course, be so widely distributed in a specific language community or culture, and be learned at so early an age, that they appear not to be constructed – the effect of an articulation between sign and referent – but to be ‘naturally’ given. Simple visual signs appear to have achieved a ‘near-universality’ in this sense: though evidence remains that even apparently ‘natural’ visual codes are culture specific. However, this does not mean that no codes have intervened; rather, that the codes have been profoundly naturalized. The operation of naturalized codes reveals not the transparency and ‘naturalness’ of language but the depth, the habituation and the near-universality of the codes in use. They produce apparently ‘natural’ recognitions. This has the (ideological) effect of concealing the practices of coding which are present.- CAT - 2024
- Para Summary
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Comprehending a wide range of emotions, Renaissance music nevertheless portrayed all emotions in a balanced and moderate fashion.
Paragraph: A volume of translated Italian madrigals were published in London during the year of 1588. This sudden public interest facilitated a surge of English Madrigal writing as well as a spurt of other secular music writing and publication. ___(1)___. This music boom lasted for thirty years and was as much a golden age of music as British literature was with Shakespeare and Queen Elizabeth I. ___(2)___. The rebirth in both literature and music originated in Italy and migrated to England; the English madrigal became more humorous and lighter in England as compared to Italy. Renaissance music was mostly polyphonic in texture. ___(3)___. Extreme use of and contrasts in dynamics, rhythm, and tone colour do not occur. ___(4)___. The rhythms in Renaissance music tend to have a smooth, soft flow instead of a sharp, well-defined pulse of accents.- CAT - 2024
- Para Completion
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: [T]he Europeans did not invent globalization.
Paragraph: The first phase of globalization occurred long before the introduction of either steam or electric power…Chinese consumers at all social levels consumed vast quantities of spices, fragrant woods and unusual plants. The peoples of Southeast Asia who lived in forests gave up their traditional livelihoods and completely reoriented their economies to supply Chinese consumers….___(1)___. These exchanges of the year 1000 opened some of the routes through which goods and peoples continued to travel after Columbus traversed the mid-Atlantic. ___(2)___. Yet the world of 1000 differed from that of 1492 in important ways….the travellers who encountered one another in the year 1000 were much closer technologically. ___(3)___. They changed and augmented what was already there since 1000. ___(4)___. If globalization hadn’t yet begun, Europeans wouldn’t have been able to penetrate the markets in so many places as quickly as they did after 1492.- CAT - 2024
- Para Completion
View More Questions